(x+58)(4x-11)=180

Solution for (x+58)(4x-11)=180 equation:

(x+58)(4x-11)=180

We move all terms to the left:

(x+58)(4x-11)-(180)=0

We multiply parentheses ..

(+4x^2-11x+232x-638)-180=0

We get rid of parentheses

4x^2-11x+232x-638-180=0

We add all the numbers together, and all the variables

4x^2+221x-818=0

a = 4; b = 221; c = -818;
Δ = b2-4ac
Δ = 2212-4·4·(-818)
Δ = 61929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{61929}=\sqrt{9*6881}=\sqrt{9}*\sqrt{6881}=3\sqrt{6881}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(221)-3\sqrt{6881}}{2*4}=\frac{-221-3\sqrt{6881}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(221)+3\sqrt{6881}}{2*4}=\frac{-221+3\sqrt{6881}}{8}
$